An intelligent analysis method for 2D CAD shapes based on CSG

doi:10.7523/j.ucas.2025.006

Abstract

Abstract:

Constructive solid geometry （CSG） is a geometric modeling technique that defines complex shapes through Boolean operations between basic geometric primitives. However， reverse modeling to recover the CSG construction sequence from existing geometric shapes has been a challenging research problem. In this paper， we propose a Transformer-based deep network architecture that can parse input geometric shapes and output their corresponding CSG modeling sequences. Using the CSGNet algorithm as a baseline， we first expanded the synthetic dataset used for training， enabling the model to learn and parse a broader range of shapes. Additionally， we adopted an autoregressive learning architecture with a VGG encoder and a Transformer decoder， leveraging the attention mechanism to better correlate the generated sequences. This approach translates 2D shape inputs into CSG sequence outputs in a fixed format， resulting in improved reconstruction quality. We also introduced a validity correction module to ensure that the model does not output invalid reconstruction sequences. Experimental results show that the proposed model achieves better quality on both synthetic and real CAD datasets.

Key words: constructive solid geometry（CSG）, attention mechanism, deep learning, validity correction

CLC Number:

Zhuohang FENG, Liyong SHEN. An intelligent analysis method for 2D CAD shapes based on CSG[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(5): 603-613.

Figures/Tables 10

Fig.1 Two different CSG construction sequences of the same 2D shape

Fig.2 Network structure and training framework

Fig.3 Prediction correction module flowchart

Table 1 Data generation rules

类别	符号表示及说明
形状(S)	圆形(c)、三角形(t, T)、正方形(s)、椭圆形(e, E)
操作(O)	并集(+)、交集(*)、差集(-)、终止($)
基元(P)	S(X, Y, R)，由形状、坐标和半径组合表示
语法规则	任意步需满足：Max_len // 2 + 1 >= num(P) > num(O) 序列结束时需满足：num(P) = num(O) + 1
生成	开始→ P → P → P \|\| O → ···
示例 (图1)	构造序列1 (左): c(32,32,24)s(32,32,8)-c(32,16,2)-c(32,48,2)-c(16,32,2)-c(48,32,2)-$ 构造序列2 (右): c(32,32,24)c(32,16,2)c(32,48,2)c(16,32,2)c(48,32,2)+++-s(32,32,8)-$

Fig.4 Comparison of test results on synthetic dataset

Table 2 Comparison of test results on synthetic data with different sequence lengths

	$T ≤ 5$			$5 < T ≤ 9$			$9 < T ≤ 13$
	$L c e$ ↓	$I O U$ ↑	$C D$ ↓	$L c e$ ↓	$I O U$ ↑	$C D$ ↓	$L c e$ ↓	$I O U$ ↑	$C D$ ↓
CSGNet	22.865	0.289	7.385	33.082	0.266	7.238	45.356	0.308	5.320
本文方法	2.706	0.631	1.967	3.152	0.603	2.103	3.270	0.580	2.218

Table 2 Comparison of test results on synthetic data with different sequence lengths

	$T ≤ 5$			$5 < T ≤ 9$			$9 < T ≤ 13$
	$L c e$ ↓	$I O U$ ↑	$C D$ ↓	$L c e$ ↓	$I O U$ ↑	$C D$ ↓	$L c e$ ↓	$I O U$ ↑	$C D$ ↓
CSGNet	22.865	0.289	7.385	33.082	0.266	7.238	45.356	0.308	5.320
本文方法	2.706	0.631	1.967	3.152	0.603	2.103	3.270	0.580	2.218

Fig.5 Comparison of test results on CAD dataset

Table 3 Comparison of numerical results for different metrics on CAD dataset

	$I O U$ ↑	$C D$ ↓	$R$ ↑
CSGNet	0.447	2.304	0.614
CSGNet-RL	0.626	1.120	0.768
SWRNet	0.551	1.402	0.748
PLAD	0.699	0.903	0.821
本文方法	0.733	0.765	0.846

Table 3 Comparison of numerical results for different metrics on CAD dataset

	$I O U$ ↑	$C D$ ↓	$R$ ↑
CSGNet	0.447	2.304	0.614
CSGNet-RL	0.626	1.120	0.768
SWRNet	0.551	1.402	0.748
PLAD	0.699	0.903	0.821
本文方法	0.733	0.765	0.846

Table 4 Ablation experiment results

数据扩充	VGG-Transformer结构	预测矫正模块	$I O U$ ↑	$C D$ ↓	$R$ ↑
×	×	×	0.699	0.903	0.821
√	×	×	0.721	0.796	0.840
×	√	×	0.712	0.850	0.830
√	√	×	0.732	0.770	0.845
√	√	√	0.733	0.765	0.846

Table 4 Ablation experiment results

数据扩充	VGG-Transformer结构	预测矫正模块	$I O U$ ↑	$C D$ ↓	$R$ ↑
×	×	×	0.699	0.903	0.821
√	×	×	0.721	0.796	0.840
×	√	×	0.712	0.850	0.830
√	√	×	0.732	0.770	0.845
√	√	√	0.733	0.765	0.846

Fig.6 Comparison of the original model with the prediction correction model

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